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# Another doubts from me

is since S is defined on real numbers. So it cant be any relation because any real number that is not an integer does not fit into the relation. Please clear my doubts here

(4) (a) Let R be a relation defined on R x R by (a, b) R(c, d) if and only if ab &lt; cd.
Let S be a relation defined on R by aSb if and only if a - b is an integer.
(i) Is R reflexive? Is R symmetric? Is R antisymmetric? Is R transitive?
(ii) Is R a partial order relation? Is R an equivalence relation?
(iii) Is S reflexive? Is S symmetric? Is S antisymmetric? Is S transitive?
(iv) Is S a partial order relation? Is S an equivalence relation?
(v) If R is an equivalence relation, then give its equivalence classes. If S is an equivalence
relation, then give its equivalence classes.
[3]

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